估计方程及结构方程模型的统计推断

发布时间：2018-03-06 06:41

本文选题：Bayes经验似然　切入点：Bayes局部影响分析　出处：《云南大学》2016年博士论文　论文类型：学位论文

【摘要】：估计方程推断方法是一种应用广泛的估计方法,许多参数估计方法,如著名的极大似然法、最小二乘法以及矩估计都是它的特殊情形。估计方程最大的优点是不依赖于任何分布,在错误指定模型的情形下也可以得到可信赖的结果,具有稳健性。处理估计方程问题的常用方法有广义矩方法、经验似然方法等,其中基于经验似然方法的估计方程推断问题引起了很多研究者的兴趣。近年来,越来越多的研究者也开始在Bayes框架下考虑经验似然方法的估计方程推断问题,即Bayes经验似然方法(BEL)。Bayes经验似然方法不仅继承了传统经验似然方法和估计方程方法的优点,而且便于将可能的多层结构和参数的附加信息结合起来。本文对在估计方程下所建立的Bayes经验似然的统计推断问题及结构方程模型(SEM)的统计推断问题分别进行了研究。我们考虑了带有不可忽略缺失数据的估计方程的Bayes局部影响分析问题、基于估计方程及经验似然的Bayes变量选择问题、分位数结构方程模型(QSEM)在估计方程下的Bayes估计等一系列问题,并研究了结构方程模型的潜在变量选择问题。首先,对于带有不可忽略缺失的数据,我们在参数先验信息和缺失机制模型假设下提出BEL方法来估计未知参数。同时,建立Bayes局部影响分析方法来对数据、先验分布、估计方程和缺失机制模型等进行敏感性分析。我们提出对数据、先验分布、估计方程和缺失机制模型的单一的或同时的扰动模型,构造Bayes扰动流形来反映扰动模型的结构和扰动程度,并在不同的目标函数下利用一阶和二阶调整Bayes局部影响测度来度量各种扰动的影响。此外我们构造拟合优度统计量来检验估计方程假设的正确性。其次,我们考虑了Bayes经验似然变量选择问题,利用估计方程建立经验似然函数并利用收缩Laplace先验同时实现变量选择和参数估计。在一定的正则条件下,我们证明得参数的后验概率依概率集中在真实参数的一领域内,即参数后验概率具有相合性。再次,根据实际需要,我们建立了分位数结构方程模型,并采用Bayes经验似然方法对参数作出估计。其中我们将潜在变量视为缺失数据来处理,利用经验似然函数构造潜在变量的条件分布估计,采用线性插值法抽样插补潜在变量及通过Gibbs抽样方法获得参数的Bayes估计。最后,我们针对结构方程模型的潜在变量选择问题进行相应的研究,提出新的探索性结构方程模型,采用惩罚极大似然方法来识别潜在变量模型的结构,并在适当的惩罚函数和调节参数下,得出估计的相合性和Oracle性质。其中我们将潜在变量视为缺失数据来处理,采用ECM算法来获得惩罚极大似然估计。我们采用MM算法来实现ECM算法中的M步,采用IC_Q准则来选择调节参数,并且建立了标准误差估计。
[Abstract]:Estimation equation inference method is a widely used estimation method, many parameter estimation methods, such as the famous maximum likelihood method, The least square method and moment estimation are its special cases. The greatest advantage of the estimation equation is that it does not depend on any distribution, and can obtain reliable results in the case of misspecifying the model. General moment method, empirical likelihood method and so on, among which the estimation equation inference based on empirical likelihood method has attracted the interest of many researchers in recent years. More and more researchers have begun to consider the estimation equation inference problem of empirical likelihood method under the framework of Bayes. That is, Bayes empirical likelihood method not only inherits the advantages of traditional empirical likelihood method and estimation equation method. Moreover, it is convenient to combine the possible multilayer structure with additional information of parameters. In this paper, the statistical inference problem of Bayes empirical likelihood and the statistical inference problem of structural equation model are discussed respectively. In this paper, we consider the problem of Bayes local impact analysis for the estimation equation with nonnegligible missing data. Based on the estimation equation and empirical likelihood Bayes variable selection problem, the Bayes estimation of the quartile structure equation model under the estimation equation, and so on, the potential variable selection problem of the structural equation model is studied. For data with non-negligible missing data, we propose BEL method to estimate unknown parameters under the assumption of parameter prior information and missing mechanism model. At the same time, we establish a Bayes local impact analysis method to analyze the data and the prior distribution. We propose a single or simultaneous perturbation model for data, prior distribution, estimation equation and missing mechanism model. The Bayes perturbation manifold is constructed to reflect the structure and degree of perturbation of the perturbation model. Under different objective functions, the first and second order Bayes local influence measures are used to measure the effects of various disturbances. In addition, we construct a goodness of fit statistic to test the correctness of the assumptions of the estimation equation. In this paper, we consider the problem of Bayes empirical likelihood variable selection, establish the empirical likelihood function by using the estimation equation and realize the variable selection and parameter estimation simultaneously by using the contraction Laplace priori. We prove that the posteriori probability of parameters is concentrated in a field of real parameters according to probability, that is, the posterior probability of parameters is consistent. Thirdly, according to the actual needs, we establish a quantile structural equation model. The Bayes empirical likelihood method is used to estimate the parameters, in which the potential variables are treated as missing data, and the conditional distribution estimation of the potential variables is constructed by using the empirical likelihood function. The linear interpolation method is used to sample the interpolation potential variables and the Bayes estimation of the parameters is obtained by Gibbs sampling. Finally, we study the potential variable selection problem of the structural equation model and propose a new exploratory structural equation model. The structure of the potential variable model is identified by using the penalty maximum likelihood method, and the consistency and Oracle properties of the estimation are obtained under the appropriate penalty function and adjusting parameters, in which the potential variables are treated as missing data. The ECM algorithm is used to obtain the penalty maximum likelihood estimation, the MM algorithm is used to realize the M-step in the ECM algorithm, the IC_Q criterion is used to select the adjusting parameters, and the standard error estimation is established.
【学位授予单位】：云南大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O212.1

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